Abstract

We survey recent developments in
dense numerical linear algebra,
covering
linear systems,
least squares problems
and eigenproblems.
Topics considered include
the design and analysis of block, partitioned and parallel algorithms,
condition number estimation,
componentwise error analysis,
and the computation of practical error bounds.
Frequent reference is made to LAPACK,
the state of the art package of Fortran software designed to solve
linear algebra problems
efficiently and accurately on high-performance computers.